Mitigating carrier phase multipath errors continue to be a significant challenge for Real Time Kinematic (RTK) using Global Navigation Satellite Systems (GNSS). As the multipath error is dependent on the operational environment and therefore cannot be mitigated by differencing techniques, we propose a Multiple Carrier Correlators based carrier phase multipath mitigation technique (MCC) for the high precise positioning in the environment with multipath. In the method, two extra carrier correlators at the phases of pi/4 and -pi/4 are introduced and a maximum likelihood estimator is developed based on these correlator outputs to estimate the carrier phase of the line-of-sight signal. A Monte Carlo simulation is carried out to evaluate the carrier phase measuring accuracy of the proposed method under multipath. The experiments using real GNSS signal data are also conducted in a certain multipath scenario and an urban canyon area with random multipath. The results show the proposed method can greatly improve the performance of Real Time Kinematic positioning in the situation with multipath and outperforms the traditional multicorrelator based carrier phase multipath mitigation method.